Interpolating function and Stokes Phenomena

TL;DR

This paper investigates the analytic structures of interpolating functions constructed from different expansions of physical quantities, revealing insights into their analytic properties and Stokes phenomena, with applications to specific models and comparisons to resurgence analysis.

Contribution

It introduces a framework linking interpolating functions' analytic structures to physical properties and Stokes phenomena, with explicit checks on zero-dimensional models and Borel plane considerations.

Findings

Interpolating functions encode information about Stokes phenomena.

Explicit analysis performed on zero-dimensional $\

Comparison made with resurgence analysis results.

Abstract

When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional $\varphi^4$ theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.